Sometimes they did. For example the [Pantheon](https://en.wikipedia.org/wiki/Pantheon,_Rome) in Rome was converted from a pagan temple to a Catholic church and was repaired as necessary over the years, so it’s still in very good condition today.
What’s more common though is that ruined buildings get taken apart for their materials. The stones or rubble can be used in new walls or as landfill. Or if they’re artistically cut pieces, they’ll look nice on your snazzy new building somewhere else. And you can use the foundation to build something new on top, something more suited for current needs than the building that used to be there. Besides, you probably don’t know exactly how it used to be, so it would be hard to recreate if you wanted to.
The ruins we have today were preserved for some reason–maybe they were buried by new construction, or by a natural disaster. Maybe nobody lives there anymore and so anything that survived the elements remained as it was. Archeologists today usually don’t want to mess with study sites too much (though historically they often did), because this can destroy evidence–moving things out of place, or causing confusion between original pieces and newer imitations, makes it harder to understand the builders of the past.
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